Updated December 29, 2015

Intro to GTM

I'm Greg Troderman, and this is gtMath (hereafter referred to as "GTM"). Welcome! As far as I know, most people reading this already know me, but for those who don't, I was a math major and physics minor at Dartmouth and am now a commodities banker. I've been trying to convince people that math is sweet since, in my first failed mission (to explain solving for $x$ to my first-grade classmates), I was booed off stage. The reason: I said "minus" instead of "take-away." #smh

Well, 19 years later, this is take $n$ of the same production. The stated goal of GTM is to show that math is NOT AT ALL about grinding numbers, but rather (in my opinion) about using logic and abstraction to distill things down to their most important properties, tie together seemingly unrelated topics, and thereby draw conclusions that may be of interest for all sorts of purposes (if not just intellectual curiosity).

You do not need to be a math genius or have gotten an A in high-school algebra to read GTM. You might need to "use your noodle," as PB&J Otter so eloquently put it.

Any prerequisite knowledge is listed and linked at the beginning of each post and covered in separate posts with the label "Prerequisites" for those who need a refresher or to whom the topic is new; I've tried to lay it out so that you can easily find all the information you'll need if you don't know it already.

If you do not find everything you need or don't understand the way I've explained it, I will try to respond to all questions posted in the comments sections and either offer an alternative explanation or provide examples. I do not intend to write, for example, an entire calculus course on here, so for the harder posts (see below), a higher level of background knowledge is assumed, but once again, I welcome requests for clarification in the comments sections and will try to address all such requests. The easier posts should not require anything you can't find on GTM itself.

Realizing that not every post will appeal to every reader, my current approach is to vary the themes and difficulties of posts as topics occur to me (or are requested) and continue to gather feedback. More on all this below...

Posts to Date; Stats

With 16 posts published as of today, I've tried to vary the difficulty of posts from easier concepts that appear in job interview brain teasers and graduate school admissions tests (e.g. the locker problem and Stars and Bars, the latter also being the answer to the first official reader request), to physics (Brownian Motion, which, the topic's being relatively new to me, took me over a month of research, i.e. head-scratching, and writing, and which is certainly the toughest post to date- it should take a while to read thoroughly for those not already familiar with the topic).

The #1 most popular post to date (by page views), and the one of which I am most proud given that it's the only one containing my own original thinking, is The Plane in $\Bbb{R}^3$, which generalizes a (rather tough) geometry question I was asked in an interview. I have done posts on combinatorics (recursions, #2 by page views as of today; generating functions, #5 as of today and an incredibly clever idea which perfectly illustrates the "tying together" I mentioned in this page's intro), and posts on basic (#3 as of today) and more advanced pool, which were all popular with readers I surveyed informally.

2015 Review; Outlook for 2016

If at least one not-traditionally-nerdy reader finishes a post and says (not just out of cordiality, or the deeply-ingrained desire not to offend), "Hmm, that was kinda neat," then the blog will have been a success. Actually, if there is at least one not-traditionally-nerdy reader, that would be a success in its own right.

As of today, based on page-view stats and my asking around, I estimate 5-10 regular, non-nerd readers and anywhere from 25 to 50 regular readers in total. I realize that these are not very precise ranges, but unfortunately, page-view stats don't give you much. In any case, given the original goal, I think the numbers and the feedback make it clear: this was a very successful first year.

I must admit that most current readers are known to have at least a little bit of a nerd streak, so maybe I just need to accept that that's my audience and roll with it, but I'll continue to reach out to the still-closeted nerds with posts that don't require advanced knowledge whenever good topics arise. If the links above weren't shameless enough, I'll say explicitly that I want more reader requests in 2016 and am hoping to source some of these good topics that way. I also hope to put out some juicy posts that will include more abstraction and formalism.

Longer-term goals for the site include adding difficulty markers on posts (perhaps as voted by readers) and making all the pages look a bit better. At the moment, I'm working off of Blogger with a copy-pasted HTML template (ya I know it looks great, but cool your jets: I didn't make it, nor do I have any idea how to do so...), so customization is tough. Any help on these issues from actual web designers would be very welcome.

Thanks for reading and helping me make the site better. I welcome topic requests (no homework help please), suggestions on writing style and accessibility, corrections if anything is wrong or if I screw up the math symbols, and any other feedback.

Thanks again and enjoy.